[GMAT数学]-GMAT数学之概率大成篇.doc

[GMAT数学]GMAT数学之概率大成篇---想的到的简单，想不到的难！
GMAT数学10个基本概念
1、mode（众数）
一堆数中出现频率最高的一个或几个数，例如：mode of 1,1,1,2,3,0,0,0,5 is 1 and0.
2、range（值域）
一堆数中最大和最小数之差，例如：range of 1,1,2,3,5 is 5-1=4
3、mean（平均数）
arithmatic mean（算术平均数），geometric mean （几何平均数：n个数之积的n次方根）
4、median（中数）
将一堆数排序之后，正中间的一个数（奇数个数字），或者中间两个数的平均数（偶数个数字），
例如：“medianof 1,7,4,9,2,2,2,2,2,5,8 is 2”，“median of 1,7,4,9,2,5is (5 7)/2=6”。
5、standard error（标准偏差）
一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(n)。
例如：standard error of 0,2,5,7,6 is: (|0-4| |2-4| |5-4| |7-4| |6-4|)/5=2.4
6、standard variation
一堆数中，每个数与平均数之差的平方之和，再除以n，例如：standardvariation of 0,2,5,7,6 is6.8
7、standard deviation
就是standard variation的平方根.
标准方差的公式：d^2=[(a1-a)^2 (a2-a)^2 .... (an-a)^2 ]/n，d 为标准方差。
8. 三角形余玄定理
C^2=A^2 B^2-2ABCOSt，其中t为AB两条线间的夹角。
9. Y=k1X B1,Y=k2XB2，两线垂直的条件为K1K2=-1
10. 三的倍数的特点：所有位数之和可被3整除。

概率题

GMAT数学概率题是最容易掌握的一类GMAT数学题型，解决这类题，用两种主要的方法就可以解决，就是加法原则和乘法原则：问自己这个事儿完成了没有?如果完成了就是加法原则，没有完成就是乘法原则。

例子一：从北京到上海可以乘飞机(3种方案)，轮船(2种方案)，或者火车(5种方案)，问从北京到上海乘这3种交通工具共几种方案?答：既然任何一个方案都已经到达了上海，这件事儿已经完成了，所以用加法原则：3+2+5=10种

例子二：从北京到上海有2条路线，从上海到深圳有5条路线，问从北京出发经由上海到深圳会有多少种路线?答：当你到达上海时还没有到达深圳呢，没有完成，那就乘起来，用乘法原则：
2×5=10
题目大讨论

求一道概率题

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概率题，求解

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1. In how many ways can 9 people be seated in a row of chairs if two of the people, David and Becky, refuse to sit together?

2. A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

3. Cain prepared 4 different letters to be sent to 4 different addresses. For each letter, he prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, 1) what is the probability that only 1 letter will be put into the envelop with its correct dress? 2)that no letter will be put into the envelope with its correct address? 3)that all letters will be put into the envelope with its correct ad dress?

4. There are y different travelers who each have a choice of vacationing at one of N different destinations. What is the probability that all y travelers will end up vacationing at the same destination?

5. A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

6. A certain basket contains 10 apples, 3 of which are green and 7 of them are red. If three different apples are selected at random from the basket, what is the probability that 2 of them are red and 1 of them is green?

7. A certain telephone number has seven digits. If the telephone number has the digit zero exactly 3 times, and the number 1 is not used at all, what is the probability that the phone number contains one or more prime digits.

8. Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person sub committees, what percent of all the possible subcommittees that include Michael also include Anthony?

9. Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

10. A committee of three people is chosen from five married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

11. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?

12. A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

13. Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

14. A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

15. A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?

16. A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?

17. The oasis output of Abu Ilan in the heart of the Negev desert, has a population of 20 Bedouin tribesmen and 20 Farma tribesmen. El Kamin, a nearby oasis, has a population of 32 Bedouin tribesmen and 8 Farima tribesmen. A lost soldier (from another country), accidentally seperated from his army unit, is wandering through the desert and arrives at the edge of one of the oases. The soldier has no idea which oasis he has found, but the first person he spots from a distance is a Bedouin. What is the probability that he wandered into Abu Illan? What is the probability that he is in El Kamin?

18. A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit target

19. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?

20.a jar contains only x black balls and white balls. One ball is drawn randomly from the jar and is not replaced. A second ball is then drawm randomly from the jar. What is the probability that the first ball drawn is black and the second ball drawn is white?

21.4对夫妇，从中任意选出3人组成一个小组，不能从任一对夫妇中同时选择两人。问符合条件的概率是多少？

22.从6双不同的手套中任取4只，求其中恰有一对配对的概率?

23.3个打字员为4家公司服务，每家公司各有一份文件录入，问每个打字员都收到文件的概率?

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特别版块---易错难题，不要被难倒了哦！

Last Sunday a certain store sold copies ofNewspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and thestore sold no other newspapers that day. If r percent of the store’s revenuesfrom newspaper sales was from Newspaper A and if p percent of the newspapersthat the store sold were copies of newspaper B, which of the followingexpresses r in terms of p?

A. 100p / (125 – p)
B. 150p / (250 – p)
C. 300p / (375 – p)
D. 400p / (500 – p)
E. 500p / (625 – p)

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